To perform a geometric translation, you need to add the same values to the x-coordinates (horizontal translation) and subtract the same values from the y-coordinates (vertical translation) of each vertex.
In this case, you need to translate the polygon 4 units to the right and 5 units down.
Let's apply the translation to each vertex:
Vertex 1: (-5, 3)
Horizontal translation: +4 units (add 4 to x-coordinate)
Vertical translation: -5 units (subtract 5 from y-coordinate)
Translated vertex 1: (-1, -2)
Vertex 2: (-1, 3)
Horizontal translation: +4 units
Vertical translation: -5 units
Translated vertex 2: (3, -2)
Vertex 3: (1, 0)
Horizontal translation: +4 units
Vertical translation: -5 units
Translated vertex 3: (5, -5)
Vertex 4: (-3, 0)
Horizontal translation: +4 units
Vertical translation: -5 units
Translated vertex 4: (1, -5)
Therefore, the translated polygon has vertices at (-1, -2), (3, -2), (5, -5), and (1, -5).